Effects of bending stiffness and support excitation of the cable on cable rain-wind induced inclined vibration

The main objective of this paper is to investigate the responses of the inclined cable due to rain-wind induced vibration (RWIV) considering the bending stiffness and support excitation of the cable. The single-degree-of-freedom (SDOF) model is employed to determine the aerodynamic forces. The 3D model of a cable subjected to RWIV is developed using the linear theory of the cable oscillation and the central difference algorithm in which the influences of wind speed change according to the height above the ground, bending stiffness, and support excitation of the cable are considered. The numerical results showed that the cable displacement calculated by considering cable bending stiffness in RWIV is slightly smaller than in the case of neglecting it. And, the cable diameter had a nonlinear relationship with cable displacement, where when both diameter and mass per unit length of cable increase cable displacement will decrease. In addition, the periodic oscillation of cable supports extremely increases the amplitude of RWIV if its frequency is nearby that of the cable. Keywords: 3D model; inclined cable; rain-wind induced vibration; rivulet; analytical model; vibration.

Multiple Parametric Resonances of Taut Inclined Cables Excited by Deck Vibration

A mechanical model is proposed to describe the vibration of a taut inclined cable excited by a deck. The dynamic system is simplified into a one-degree-of-freedom nonlinear system with non-dimensional parameters by using the Galerkin and non-dimensional analysis methods. The periodicity ratio (PR) method is improved and applied to the parameter analysis for the cable system. The frequency ratio between the natural frequency of the cable and the vibration frequency of the deck and the amplitude of deck vibration are the main variable parameters, and nonlinear motion is diagnosed for a large range of parameters. Several forms of motion are distinguished, and the evolution between the forms is studied. Meanwhile, several types of parametric resonance are revealed in different ranges of parameters. The results indicate that the parametric resonance in the case of a 3:2 frequency ratio is significant and should be given more attention.

Nonlinear Dynamics Analysis for the Taut Inclined Cable Excited by Deck Vibration

A simple mechanical model is proposed to describe the dynamics system of the taut inclined cable excited by the deck vibration. Using Galerkin method, the dynamics system is simplified into a one-degree of freedom nonlinear system. Average method is used to obtain the average equations and bifurcation equation. Bifurcation maps are obtained and used to reveal the evolution mechanism of period-1 motion to period-2 motion. Several motion forms are discussed and evolution progress between different motions is studied. Several kinds of parametric resonance are revealed in various parameter regions. The conclusions indicate that the parametric resonance excited by the frequency ratio 3:2 is significant should be paid more attention.